Design The Resilient Controller And Filter Based On Finite-time Stability

In the process of system analysis and control,the stable performance is the core condition that control system can function normally.However,in the process of system description and design,due to the influence of measurement error,modeling error or interference signal,the system model can not avoid uncertainty and time delay,both of which will affect the stable operation of the system.The robust control is to extract the uncertain items which contain interference in the control system,and design the controller in the range of interference allowable fluctuation,so that the system has high stability performance index and robustness.Therefore,the robust control theory has been favored by scholars and has been fruitful in the field of control in recent years.However,it is necessary to explain that the robust stability of the existing literatures is based on the Lyapunov stability theory and described the steady state characteristics of the system in a infinite-time interval.In fact,in the process of system control,it is necessary to consider the short time control problem,namely the control of the system in a limited short time.Based on this,in 1961,Dorato presented the concept of finite time(or short time)stability.Comparing with the concept of Lyapunov stability,the difference is that the finite time stability focuses on the state trajectory characteristics and transient performance of the system in a given finite-time interval.In recent years,the concept of finite-time stability has been widely concerned,and in the fields of linear systems,time-delay systems and stochastic system,related to:finite time bounded,finite time stabilization,finite time control and finite time filtering.However,the finite-time resilient control and filtering problem of linear systems with uncertainties and time-delays is not well studied.Therefore,it is necessary to analyze the dynamical system with time-delays and uncertainties.In this paper,applying Lyapunov function studies the resilient controller and filter design problems and the main research contents are as follows:(1)The finite time resilient H? control problem of a class of uncertain systems with time-delays are studied.The-finite time resilient H? controller is designed and the sufficient condition is obtained by selecting the appropriate Lyapunov equation.At the same time,the finite-time controller gain is obtained by applying linear matrix inequality techniques in MATLAB,and transforms it into an optimization solution problem.(2)The finite-time resilient L2-L? control problem of a class of uncertain systems with time-delays is considered.Meanwhile,the finite-time L2-L? controller gain in MATLAB is obtained by using the method of linear matrix inequality,and then transforms it into an optimization solution problem.(3)For a class of time-delayed uncertain systems,it designed the resilient H?filter based on the finite-time bounded theory,and several inequalities are transformed into simple optimization problems,it also proves by a set of simulation examples.(4)For a class of systems time-delayed uncertain systems,a sufficient condition to solve the resilient L2-L? filter is presented and obtained.A simulation example is give at last to show the effectiveness of the design method.